Darkhan: Note: the trading dock also can serve as extra resource storage for emergencies as long as you don't trade those resources away :)
You know, while I've done it in small amounts occasionally, I hadn't thought of doing that in any serious fashion. But I've been trying to stockpile food/other things in my last map before I start serious expanding and keep having to build barn after barn. I shall try the trading post/s as storage trick, thanks. :)
As to the original question - pretty much what Kardwill said. Build slower, let resources pile up before using them up. A lot of the buildings that require a lot of stone aren't necessary to build early on, for example. You can put down the "blueprint" of something to build and then pause it so it's not actually built/no resources are taken yet, if you're trying to plan layouts.
A Forester is helpful, should at least have one of those early on.
If loose stone isn't abundant on the map you're on, build a quarry as soon as able. It's slow, but it does get you the stone you want eventually. Or a trading post and patiently wait for the boat who trades stone to visit, as you're stockpiling something to sell/trade for it.